Question

I wanted to discuss a problem with someone.
Topic:- Vectors

Answer 1

A particle is kept at rest at origin. Another particle starts from (5,0) with a velocity -4i +3j. Find their closest distance of approach

Answer 2

so you don't want to discuss it anymore?
"wanted"

Answer 3

Why i want to
I got the answer to this question , however i feel my method needs to be checked

Answer 4

It sounds like you just need to find the minimum distance between the particles. The moving particle travels along a line. Find the equation of the line and it's fairly simple calculus from there.

Answer 5

closest distance = perpendicular distancce

Answer 6

Okay @ganeshie8 Continue ,
So is it trig

Answer 7

like everything in math, it can be done many ways, S&G gave you calculus method using optimization earlier

Answer 8

Yes ,

Shall i show my approach

Answer 9

yeah please :)

Answer 10

There is a formula given in my book
Closest distance of approach =
\[\huge \left| \frac{ r_{12}*v_{12} }{ v_{12} } \right|\]

Answer 11

Where r denotes the position
v is the velocity of the particles

Answer 12

\[\huge r_{1} - r_{2} = (0i+0j)-(5i+0j) = -5i+0j\]

Answer 13

\[\huge v_{1}-v_{2}=(0i+0j)-(-4i+3j)= 4i-3j\]

Answer 14

\[\huge v_1 - v_2 = 4i - 3j \]

Answer 15

\[\huge r_1 - r_2 = -5i + 0j\]

Answer 16

\[\left| v_{12} \right| = \sqrt{4^{2}+(-3)^{2}} = 5 \]